Mathematical Sciences: Representations of Forms in Several Variables

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This research is concerned with the study of real and complex forms by means of a natural inner product. The principal investigator will examine sums of even powers of forms; spherical designs; sums of powers of complex linear forms; sums of cubes of linear forms; inequalities for products of forms; and symmetric forms. The research supported involves the theory of forms. This is the study of homogeneous polynomials over the real numbers or over the complex numbers. The study of real and complex forms has deep interrelations with linear algebra, combinatorics, number theory, algebraic geometry, functional analysis and numerical analysis.